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Abstract

Systematic errors specific to a snapshot Mueller matrix polarimeter are studied. Their origins and effects are highlighted, and solutions for correction and stabilization are proposed. The different effects induced by them are evidenced by experimental results acquired with a given setup and theoretical simulations carried out for more general cases. We distinguish the errors linked to some imperfection of elements in the experimental setup from those linked to the sample under study.

References

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a Phases are expressed in radians. In the ideal case (no phase errors) and for the linear polarizer at 30°, the value of the polarization parameters depolarization index (PD), diattenuation (D) and retardance (R) are (PD=1, D=0, R=0). When ϕp=0 and ϕw=0.01, these values become PD=0.989, D=0.999, and R=0.58.

Table 4

Experimental Mueller Matrix Given by the SMMP for Vacuum and a Linear Partial Polarizer at 30°: Theoretical, without Corrections by ϕw, ϕ2, ϕ3, and ϕ4 and with Corrections by ϕw, ϕ2, ϕ3 and ϕ4a

a All matrices are normalized by m00. The experimental setup is composed of two calcite plates (n=0.166) for the coding system (e=2.08mm±0.01mm) and two calcite plates for the decoding system (e=10.4mm±0.01mm). The source is a broadband spectrum source with λ0=829nm, and the analysis window of the detection system is Δλ=10nm sampled with 512 pixels.

Table 5

Simulation of the Influence of the Misalignment Errors Δθ1, Δθ2, Δθ3, Δθ4 and Δθpolon the Mueller Matrix for Vacuum

Δθpol(°)

Δθ1(°)

Δθ2(°)

Δθ3(°)

Δθ4(°)

Mueller Matrix for Vacuum

0

0

0

0

0

(1000010000100001)

0.5

0

0

0

0

(1000010.015−0.00800100001)

0

0.5

0

0

0

(100001000.015−0.0150.9820−0.0080.00800.982)

0

0

0.5

0

0

(100001.003−0.0180−0.0150.0171.01700.008001.017)

0

0

0

0.5

0

(100.015−0.008010.01700−0.0181.01700001.017)

0

0

0

0

0.5

(10−0.0150.00801−0.0150.008000.98200000.982)

0.5

0.5

−0.5

0.5

0.5

(10000.0020.9980.03400.031−0.0500.9640−0.0170.00800.965)

0.1

0.1

−0.1

0.1

0.1

(1000010.00700.006−0.010.9930−0.0030.00200.993)

Table 6

Simulation of a Quarter-Wave Plate (R=90°, α=20°) at Different Ordersa

Δϕλ/4/Δϕcoding (%)

PD

R(°)

α(°)

0.055

0.999

89.99

19.99

0.275

0.999

89.94

19.99

0.55

0.998

89.84

19.97

1.1

0.995

89.66

19.93

2.75

0.975

89.55

19.58

5.5

0.917

82.88

18.64

a Depolarization index PD, retardance R, and azimuthal angle α are calculated. The ratio between the evolution with the wavelength of the quarter-wave plate retardance and the evolution with the wavelength of the reference coding plate retardance is given.

a Phases are expressed in radians. In the ideal case (no phase errors) and for the linear polarizer at 30°, the value of the polarization parameters depolarization index (PD), diattenuation (D) and retardance (R) are (PD=1, D=0, R=0). When ϕp=0 and ϕw=0.01, these values become PD=0.989, D=0.999, and R=0.58.

Table 4

Experimental Mueller Matrix Given by the SMMP for Vacuum and a Linear Partial Polarizer at 30°: Theoretical, without Corrections by ϕw, ϕ2, ϕ3, and ϕ4 and with Corrections by ϕw, ϕ2, ϕ3 and ϕ4a

a All matrices are normalized by m00. The experimental setup is composed of two calcite plates (n=0.166) for the coding system (e=2.08mm±0.01mm) and two calcite plates for the decoding system (e=10.4mm±0.01mm). The source is a broadband spectrum source with λ0=829nm, and the analysis window of the detection system is Δλ=10nm sampled with 512 pixels.

Table 5

Simulation of the Influence of the Misalignment Errors Δθ1, Δθ2, Δθ3, Δθ4 and Δθpolon the Mueller Matrix for Vacuum

Δθpol(°)

Δθ1(°)

Δθ2(°)

Δθ3(°)

Δθ4(°)

Mueller Matrix for Vacuum

0

0

0

0

0

(1000010000100001)

0.5

0

0

0

0

(1000010.015−0.00800100001)

0

0.5

0

0

0

(100001000.015−0.0150.9820−0.0080.00800.982)

0

0

0.5

0

0

(100001.003−0.0180−0.0150.0171.01700.008001.017)

0

0

0

0.5

0

(100.015−0.008010.01700−0.0181.01700001.017)

0

0

0

0

0.5

(10−0.0150.00801−0.0150.008000.98200000.982)

0.5

0.5

−0.5

0.5

0.5

(10000.0020.9980.03400.031−0.0500.9640−0.0170.00800.965)

0.1

0.1

−0.1

0.1

0.1

(1000010.00700.006−0.010.9930−0.0030.00200.993)

Table 6

Simulation of a Quarter-Wave Plate (R=90°, α=20°) at Different Ordersa

Δϕλ/4/Δϕcoding (%)

PD

R(°)

α(°)

0.055

0.999

89.99

19.99

0.275

0.999

89.94

19.99

0.55

0.998

89.84

19.97

1.1

0.995

89.66

19.93

2.75

0.975

89.55

19.58

5.5

0.917

82.88

18.64

a Depolarization index PD, retardance R, and azimuthal angle α are calculated. The ratio between the evolution with the wavelength of the quarter-wave plate retardance and the evolution with the wavelength of the reference coding plate retardance is given.